On Bloch-Kato's Tamagawa number conjecture for Hecke ckaracters of imaginary quadratic number fields, by Bing Han

This is essentially the author's thesis submited to The University of Chicago (May 1997). It was written in amslatex. I prove the validity of Tamagawa number conjecture of Bloch-Kato for certain Hecke characters. I study the exponential map and local Tamagawa number for all odd primes (both ordinary and supersingular), using Kato's explicit reciprocity law for one dimensional Lubin-Tate formal group. I also study p-part of Shafarevich-Tate group for motives associated to Hecke characters, using Rubin's Main Conjecture in Iwasawa theory. Interestingly a congruence property between p-adic periods of elliptic curve and weight 1 Eisenstein series evaluated at torsion CM points play a crucial role in the proof of Bloch-Kato conjecture.

Bing Han <jmwang@math.uchicago.edu>